A synastry chart tells you how the two people relate to each other. So if one person has the moon conjunct the other's sun then it means they will have a good understanding of how that persons acts emotionally and feels.
A composite chart is said to describe the relationship. It's just the midpoint of each pair of planets. So a Aries Sun with a Leo Sun creates a composite Gemini Sun, so the relationship will be seen by outsiders as communicative and friendly (e.g. Gemini traits).
It also allows you to understand how the partners feel about the relationship. So if one partner had Gemini Saturn and the other Libra Saturn creating a composite Leo saturn, and this happened to be conjunct the natal sun of the Leo partner; that partner might find the relationship all a bit heavy and restrictive despite the appearance to others of the relationship as being light and fun.
You can do the charts without knowing birth times, but of course you're working with less info. You still get to know all the aspects (conjunctions, trines, sextiles) but you won't know how the Ascendents/Midheavens are affected or what houses planets fall in.
As for whether two people will meet again ... the composite chart may give good indications; I doubt the synastry chart will. But the individual charts might also show where a partner has something due to happen in their life.